The Impact of Imperfect Timekeeping on Quantum Control

In order to unitarily evolve a quantum system, an agent requires knowledge of time, a parameter which no physical clock can ever perfectly characterise. In this letter, we study how limitations on acquiring knowledge of time impact controlled quantum operations in different paradigms. We show that the quality of timekeeping an agent has access to limits the gate complexity they are able to achieve within circuit-based quantum computation. It also exponentially impacts state preparation for measurement-based quantum computation. Another area where quantum control is relevant is quantum thermodynamics. In that context, we show that cooling a qubit can be achieved using a timer of arbitrary quality for control: timekeeping error only impacts the rate of cooling and not the achievable temperature. Our analysis combines techniques from the study of autonomous quantum clocks and the theory of quantum channels to understand the effect of imperfect timekeeping on controlled quantum dynamics.Comment: 5 + 7 pages, 2 figure

DQC1 as an Open Quantum System

The DQC1 complexity class, or power of one qubit model, is examined as an open quantum system. We study the dynamics of a register of qubits carrying out a DQC1 algorithm and show that, for any algorithm in the complexity class, the evolution of the logical qubit can be described as an open quantum system undergoing a dynamics which is unital. Unital quantum channels respect the Tasaki-Crooks fluctuation theorem and we demonstrate how this is captured by the thermodynamics of the logical qubit. As an application, we investigate the equilibrium and non-equilibrium thermodynamics of the DQC1 trace estimation algorithm. We show that different computational inputs, i.e. different traces being estimated, lead to different energetic exchanges across the register of qubits and that the temperature of the logical qubit impacts the magnitude of fluctuations experienced and quality of the algorithm.Comment: 14 pages, 4 figure